Parametric Pareto Set Learning: Amortizing Multiobjective Optimization With Parameters

Abstract

Parametric multiobjective optimization (PMO) addresses the challenge of solving an infinite number of multiobjective optimization problems (MOPs), where optimal solutions must adapt to varying parameters. Traditional methods, such as parameterized multiobjective evolutionary algorithms (MOEAs), generate only a finite set of solutions and are unable to capture the continuous structure of the Pareto set (PS) across the entire parameter space, thereby leaving critical tradeoffs unexplored. To overcome these challenges, we propose parametric Pareto Set Learning (PPSL), a novel framework that leverages amortized optimization to learn a unified mapping from parameters to the PS with respect to the parameter. The framework employs a hypernetwork conditioned on input parameters, enabling real-time inference of optimal solutions for any parameter setting without the need for repeated optimization. By integrating low-rank adaptation (LoRA), parametric PSL (PPSL) achieves computational efficiency and scalability for PMO problems. To verify its effectiveness, we apply PPSL to dynamic MOPs (DMOPs) and MOPs with shared component design, where the parameters encode time-dependent or modular constraints. The experimental results demonstrate that PPSL significantly outperforms existing methods in terms of solution quality and adaptability. Importantly, we emphasize that PPSL is not limited to the two problems tested in this work; it is broadly applicable to any real-world problem that can be modeled as a PMO problem, offering a versatile and powerful solution for a wide range of applications. Code is available at: https://github.com/jicheng9617/PPSL.